A key authoritarian element of fascism is its endorsement of a prime national leader, who is often known simply as the " Leader " or a similar title, such as Duce in Italian, Führer in German, Caudillo in Spanish, Poglavnik in Croatia, or Conducător in Romanian.

In Z < sub >< var > p </ var ></ sub > for a prime number < var > p </ var >, one non-identity element can be replaced by any other, with corresponding changes in the other elements.

" A prime element of Laar's program was introduction of the flat tax.

An element p of R is called prime element if it is neither zero nor a unit ( i. e., does not have a multiplicative inverse ) and satisfies the following requirement: given x and y in R such that p divides the product xy, then p divides x or y.

In any ring R, any prime element is irreducible.

Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry.

In mathematics, given a prime number p, a p-group is a periodic group in which each element has a power of p as its order: each element is of prime power order.

Principal ideal domains are thus mathematical objects which behave somewhat like the integers, with respect to divisibility: any element of a PID has a unique decomposition into prime elements ( so an analogue of the fundamental theorem of arithmetic holds ); any two elements of a PID have a greatest common divisor ( although it may not be possible to find it using the Euclidean algorithm ).

For general groups, Cauchy's theorem guarantees the existence of an element, and hence of a cyclic subgroup, of order any prime dividing the group order ; Sylow's theorem extends this to the existence of a subgroup of order equal to the maximal power of any prime dividing the group order.

# Although technology might be a prime element in many public issues, nontechnical factors take precedence in technology-policy decisions.

By definition of prime element, if is a Gaussian prime, then it divides ( in Z ) some.

This is really the same construction, as the Stone space of this Boolean algebra is the set of ultrafilters ( or equivalently prime ideals, or homomorphisms to the 2 element Boolean algebra ) of the Boolean algebra, which is the same as the set of ultrafilters on X.

In mathematics, a unique factorization domain ( UFD ) is a commutative ring in which every non-unit element, with special exceptions, can be uniquely written as a product of prime elements ( or irreducible elements ), analogous to the fundamental theorem of arithmetic for the integers.

In abstract algebra, an element of a commutative ring is said to be prime if it is not zero or a unit and whenever divides for some and in, then divides or divides.

Equivalently, an element is prime if, and only if, the principal ideal generated by is a nonzero prime ideal.

It was his prime example of synthetic a priori knowledge ; not derived from the senses nor deduced through logic — our knowledge of space was a truth that we were born with.

Set in the closing months of 1899, it features the eponymous private detective agency investigating a conspiracy to blow up a train, and their prime suspect's efforts to find the truth.

At the Azores conference of 16 March, Tony Blair, George W. Bush, and Spanish prime minister José María Aznar announced the imminent deadline of 17 March for complete Iraqi compliance, with statements such as " Tomorrow is a moment of truth for the world ".

Likewise, James McDonald has expressed the view that extreme groups undermined serious scientific investigation, stating that a " bizarre ' literature ' of pseudo-scientific discussion " on " spaceships bringing messengers of terrestrial salvation and occult truth " had been " one of the prime factors in discouraging serious scientists from looking into the UFO matter to the extent that might have led them to recognize quickly enough that cultism and wishful thinking have nothing to do with the core of the UFO problem.

So, the truth of the Agoh-Giuga conjecture combined with Wilson's theorem would give: a number p is prime iff

The investigation of what happened in Iraq is of prime importance to restore truth and preserve collective memory against the constant rewriting of history.

He was a founding member and a prime mover in the foundation of the Institution of Mechanical Engineers in 1847, but there is no truth in the long-standing report that the institution was founded in his house in Manchester ( it was in fact founded at the Queens Hotel at Curzon Street railway station in Birmingham ).

To account for the fact of synthesis in cognition, in express opposition to associationism, as represented by Hume, was, in truth, his prime object, starting, as he did, from the assumption that there was in knowledge that which no mere association of experiences could explain.

This result would also follow from the truth of the twin prime conjecture.

" However, the locus of the celebrations is the national capital, Ottawa, Ontario, where large concerts and cultural displays are held on Parliament Hill, with the governor general and prime minister typically officiating, though the monarch or another member of the Royal Family may also attend or take the governor general's place.

Any rational number with a denominator whose only prime factors are 2 and / or 5 may be precisely expressed as a decimal fraction and has a finite decimal expansion.

A heat engine may also serve as a prime mover, a component that transforms the flow or changes in pressure of a fluid into mechanical energy.

The regular parliamentary term is four years ; however, the president may dissolve the eduskunta and order new elections at the request of the prime minister and after consulting the speaker of parliament.

1 may be inserted without changing the value of n ( e. g. 1000 = 2 < sup > 3 </ sup >× 3 < sup > 0 </ sup >× 5 < sup > 3 </ sup >). In fact, any positive integer can be uniquely represented as an infinite product taken over all the positive prime numbers,

The segment would always open up spoofing Burma-Shave road signs as some of the Hee-Haw cast were seen piled on a truck driving down the road to Slim's Bar-B-Q whose guests often complained about the food to which Slim would counter with something like " I may not have prime meat at this picnic but I do have prime entertainment ..." and then he'd bring out the entertainment.

that may give a head of state or their representative additional powers in unexpected circumstances ( such as the dismissal of Australian prime minister Gough Whitlam by Governor-General Sir John Kerr.

Depending on the function, the remainder may be uniform only for certain values of n, e. g. odd or prime numbers.

Above all, in time of peace this is fine, but when there is a fear that there may even be a war, then more importantly, considering the welfare of the imperial house, I wonder about the wisdom of a member of the imperial family serving prime minister.

But the Arms Park site is a prime piece of real estate in the centre of Cardiff, which means that it may be difficult to sell the land to property developers.

In many systems, the prime minister selects and may dismiss other members of the cabinet, and allocates posts to members within the government.

As well as being head of government, a prime minister may have other roles or titles — the Prime Minister of the United Kingdom, for example, is also First Lord of the Treasury and Minister for the Civil Service.

In this system, as in the Parliamentary system, there are both a president and a prime minister ; but unlike the parliamentary system, the president may have significant day-to-day power.

The lifespan of parliament is limited by the constitution to five years and, though the governor general may still, on the advice of the prime minister, dissolve parliament and issue the writs of election prior to the date mandated by the Canada Elections Act ; the King-Byng Affair was the only time since Confederation that the viceroy deemed it necessary to refuse his prime minister's request for a general vote.

If, however, an opposition party wins a majority of seats in the House of Commons, the prime minister may resign or be dismissed by the governor general.

There do exist checks on the prime minister's power: parliament may revoke its confidence in an incumbent prime minister ; cabinet or caucus revolts can quickly bring down a sitting premier, and even mere threats of such action can persuade and / or compel a prime minister to resign his post, as happened with Jean Chrétien ; the Senate may delay or impede legislation put forward by the Cabinet, such as when Brian Mulroney's bill creating the Goods and Services Tax ( GST ) came before the upper chamber ; and, given Canada's federal nature, the jurisdiction of the federal government is limited to areas prescribed by the constitution.

" Either the sovereign or his or her viceroy may therefore oppose the prime minister's will in extreme, crisis situations.